Question

The product of the first three numbers in GP with non-fractional common ratio is 216. What are the numbers. If it has 15 terms? What is its sum.​

Answer 1

Answer:

Let the numbers are ar,aandar.

Then, ar⋅a⋅ar=216

⇒a3=216⇒a=6

Also,

ar(a)+a(ar)+ar(ar)=156

⇒a2(1r+r+1)=156

⇒1+r+r2r=156a2

⇒1+r+r2r=15636

⇒1+r+r2r=133

⇒3+3r+3r2−13r=0

⇒3r2−10r+3=0

⇒3r2−9r−r+3=0

⇒(3r−1)(r−3)=0

⇒r=13orr=3

So, the three numbers are , 2,6and18.

Answer 2

༼ Answer ༽

let a/r, a, ar are in GP

A/C to question,

(a/r) a ar = 216

a³ = 216

a³ = (6)³

a= 6

again,

sum of their products in pair = 156

(a/r) a + ax ar + arx (a/r) = 156

a²/r+ a²r + a² = 156

36/r+36r+ 36 = 156

36(1/r+r+1) = 156

3(r² +r+ 1) = 13r 3r²+ 3r+ 3-13r = 0

3r²-10r+ 30

3r²-9r-r+ 3 = 0

r = 3 and 1/3

so, numbers are 6/3, 6, 6x3 => 2, 6, 18 numbers are 6x3, 6, 6/3 => 18, 6,2

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